I've seen lots of 3-legged dogs, but I've never seen one with a prosthetic leg, does she have to go through physical therapy to learn how to use it, just like people do?

We'll have to see. We'll likely do physio prior to getting the prosthesis to keep the range of motion and muscle tone in the shoulder, maybe do some electrotherapy to stimulate muscle development. I imagine that we'll have to gradually work her up to using the prosthesis for longer periods of time, just as we had to develop her strength gradually with her good front leg over the past few months.
Prostheses for dogs aren't common, but more vets are becoming aware of them as an option. Here's some pics: